Consider the following scenario analysis of the economy: Rate of Return Scenario Probability Stocks Bonds Recession 0.2 -5% 14% Normal 0.6 15% 8% Boom 0.2 25% 4% i) Calculate the expected return and standard deviation of each investment (7 marks) (ii) What is the rate of return in each scenario of a portfolio that is 60% invested in the stock and 40% in the bond? (3 marks). (iii) What are the expected return and standard deviation of the portfolio? (4 marks) (iv) Would you prefer to invest in the portfolio, in stocks only, or in bonds only? (2 marks) (v) Calculate the correlation coefficient for the bond and stock returns (3 marks). b) Suppose an investor has $50,000 to invest in a portfolio of risk-free asset and the market portfolio. The expected return on the market portfolio is 13.5 percent and the risk-free rate is 4.25 percent. How much of the funds should be in the risk-free asset if the portfolio has an expected return of 10 percent?